Mechanical fire control computer, solving trigonometric equations



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MECHANICAL FIRE CONTROL COMPUTER SOLVING TRIGNQMETRIC EQUATIONS Feb. 6, 1962 11.5 Sheets=-Shes t 14 Filed Nov. 4, 1949 Laws 14/: 1M M- Gtkornegi United. States The present invention relates to computers ofthe linkage network type andmore' particularly to a computer of this type for the solution of trigonometric equations.

Bar linkages are adaptable to the performance of a wide variety of calculations and the generation of a substantially unlimited number of mathematical functions. By grouping such linkage together or combining them with other computing components they can be used to solve many complex mathematical problems. the creating of such combinations presents the problem of avoiding an increase in structural complexity proportionate to the complexity of the calculation to be effected.

- The present invention is directed primarily toward the provision of linkage networks for the solution of simul= taneous trigonometric equations whereby the unknown sides, or angles, or the area of a triangle of any shape may be determined from data sufiicient to compute these values by trigonometry. One useful embodiment of the invention is disclosed as an anti-aircraft barrage fire control computer, in which form the present invention was disclosed in my copending application, Serial No. 444,- 573, filed May 26, 1942, now abandoned, of which the present application is a continuation in part. However,

However;

atent' of the item entering means and the parts immediately the complexity of such a computer is so great that it is 7 much more difi'icult'to understand certain fundamental aspects of the invention therefrom, and there is also d1s-= closed herein, therefore, a general purpose triangle solverv which is of simpler construction while embodying many of the same principles.

The general purpose triangle solver herein disclosed employs a combination of two right-triangle solving mechanisms to solve a triangle other than a right-triangle; this being feasible because any triangle may be di vided into two right-triangles each having one side equal to the altitude of the divided triangle. Area is calculated by solving the equation:

/zR, sin a(V cos 5+R, cos e)=ar'ea where V and R, are each a hypotenuse of one right triangle, and a and 13 are the undivided angles of the di vided triangle. The divided side of the original nonright-triangle, designated C, is calculated by solving the equation: 1

Any of the quantities V, R,, c: or 13 which may be un known (the other three being known) is determined by balancing the equation:

V sin El-R sin =0 The same equation-balancing principles are employed in the anti-aircraft barrage fire control computer, but since the mathematical treatment is much more complex it will be set forth in the detailed description of this embodiment, hereinafter.

The invention, together with additional objectives and advantages thereof, will be best understood from the following description when read in connection with the accompanying drawings.

FIGURE 1 is a front elevational view of the computer;

FIGURE 2 is a rear elevational view with the levers and links being shown in the positions corresponding to the zero setting of the various item entering knobs;

FIGURE 3 is a view similar to FIGURE 2, but show "ice 2 ing the parts in their respective positions when items have been entered by the item entering knobs; FIGURE 4 is an enlarged cross-sectional plan view on the line 4-4 of FIGURE 2;

FIGURE 5 is an enlarged cross-sectional view of one associated therewith;

FIGURE 6 is an end view of FIGURE 5;

I FIGURE 7 is an enlarged cross-sectional view on the line 7-7 of FIGURE 1, and with the slantrange pointer rotated to its approximately eleven thousand yard posh tion;

FIGURE 8 is a rear elevational view of the parts which are movable by the actuation of the target posi tion angle knob;

FIGURE 9 is a rear elevational view of the parts which are movable by the actuation of the barrage time knob and. the preparation time knob;

FIGURE 10 is a rear elevational view of the parts. which are moved by the altitude knob;

, FIGURE 11 is a rear elevational view. of the. parts movable by theactuation of the deflection spot knob, the powder fuze spot knob, and the elevation spot knob;

FIGURE 12 is a rear elevational view of theparts moved by the actuation of the-target speed knob; I

FIGURE 13 is a rear elevational view of the parts ac tuated by the advance position angle knob; I

FIGURE 14 is a rear elevational view of the parts moved by the mechanical fuze setting knob; r FIGURES 15, 16 and 17are" geometrical diagrams to FIGURE. 18 with the rear cover removed to expose the mechanism;

FIGURE 20 is a front view thereof with the face plate, dial plate and top plate removed to expose underlying parts; and

FIGURE 21 is a partial sectional view line 2121 o FIGURE 20.

Considering. first, the anti-aircraft barrage fire control taken on the computer of FIGURES 1 to 17, inclusive, the present invention is designed to provide the necessary data for directing a barrage of predetermined duration in such a way as to intercept an attacking plane. The mathe matics of this problem are dia'grammed in FIGURES 15, 16 and 17'.

Referring to FIGURE 15, let it be presumed that the operator at firing station 0 observes the approaching plane at A. As a matter of fact, the operator has first observed the plane prior to its reaching the point A, has identified the type of plane so that he knows its cruis ing speed of Vp, as well as its altitude it.

Let it further be presumed that the plane will main tain this altitude and will fly directly over the point 0, releasing its bombs so as to strike the point 0. The operator also knows the velocity, 'Vb, of the projectile. The operator will require some period of time in order to operate the calculator so as to secure the desired data half of the barrage time the plane would have advanced to the point C, the distance BC being l/2TbVp. While the plane progresses from B to C, the gun is constantly fired. When it arrives at the point C, which is the position of the plane when the midshot of the barrage is fired, the projectile is tired which should make a direct hit at the point D.

The gun is at all times pointing in advance of the telescopic sight trained on the plane. For instance, when the plane is at C, the telescopic sight would be along the line C, but the gun would be pointing along the line OE. The projectile wouldbe propelled from the gun along the line OE, but its trajectory would cause it to deviate from the line OE to the point D along the dotted line.

Obviously the dotted line CD, which at its lower end coincides with the line OE, is a longer line than the direct line OD, but the difference is very small and the average velocity of the bullet, or projectile Vb, is considered as though it had travelled the straight line OD.

The length of the line OD is obviously the velocity of the projectile Vb multiplied by t, which is the time in seconds set for it to explode. Since the shot fired when the plane was at the point C is supposed to meet the plane at the point D, and to explode directly at the plane, the distance DC is equal to the velocity of the plane, Vpxi, or Vpt.

As the plane continues its movement, in case. it is not brought down, from D toward F, the barrage would continue so that the entire barrage, or the line indicating the bursts, is L L which is theoretically an arc having'a center 0 and a radius OD. It will be noted that the first burst at L is below the position of the plane it the plane continued at a uniform altitude h, while the last part of the barrage from D to L would cause explosions to take place above the altitude h.

The reasons are twofold. First, explosions cannot be predicted precisely. Two projectiles having exactly the same fuze setting and firing along the same line, might explode at slightly different points. Some of the explosions might, therefore, occur anywhere between slight ly below or slightly above the are L L The second reason is, that the pilot will notice that he is flying into an anti aircraft barrage, and he might dive. In that case he would dive directly into that part of the barrage between D and L On the other hand, he might climb, in which case he would climb into that part of the barrage between D and L1.

The angle (a) is known as the sight elevation angle, or the super elevation angle, and means that the gun actually points at an angle (a) from where it is expected that the projectile will explode. In FIGURE 15, therefore, the gun is pointed along the line OE, whereas the explosion will take place at D, and the angle between the lines OE and OD is angle (a). The lead angle (1)) represents the amount of divergence between the line OC, which represents the telescopic sight between the station 0 and the then position of the plane at C and the line OD, which represents the straight line between the station 0 and the point of the burst of the projectile being fired.

The sight angle is the sum of a, plus b, and is the angle between the telescopic sight trained on the plane and the actual direction in which the gun is trained. The angle 0 and d are not calculated in the computer and are useful merely in describing FIGURE 15.

The angle (e) is the target position angle and repre sents the angle formed by the horizontal line from O and the line drawn from O to A, it being remembered that the point A is the position of the plane when the operator starts his calculations. The angle (g) is the advance position angle and is the sum of angles b, c, d, and e, or is the angle formed between the horizontal line from O and the line OD, it being remembered that the point D is the point of the explosion ot the projectileat the middle of the barrage. The line OA will generally, hereafter, be referred to as Rs, meaning slant range. It will, therefore, be remembered hereafter that slant range is the distance from the station 0 to the point A which is the position of 5 the plane at the commencement of the preparation time,

From; this, FIGURE 15, one of the formulas which is involved may be directly calculated. Obviously, sin g equals so that OD(sin g)=h. However, the line OD is equal to Vbt, so that Vb! sin g-h=0. Formula No. i.

In FIGURE 17 the line DA is obviously the sum of the lines DC, plus CB, plus BA of FIGURE 15, or

The angle sin P sin Q l p(' g+ Tx+ t) DN 40 Therefore Tbs-H) DN=sin QVp W However, I

' g+e l-1a sin Q-s m (Q0 )cos 2 and g-e ge sin P-Sll1 (9O cos 2 Therefore 00S V17 TIC-Ft) DN= COS 50 Therefore, 0A, or Rs, that is the slant range, is equal to:

Tb cos i Vp(- +T.v+t +Vbt cos Y 2 Formula l o. 2

Referring again to FIGURE 15, it will be noted that sin c= or h=R, sin e Formula No.3

The reasons that Formulas 1 and 3 are written so as to equal is because, as will hereinafter be explained, the target position angle balance pointer 85 is balanced at a zero position, which is at its midposition, and the advance position angle balance pointer- 138 is likewise balanced at its zero or midposition. In operating the computer, no reading should be taken. until the said pointers 85 and 138 are both in their zero or rnidpositions.

In firing projectiles, it is well known that they rotate on their axes which, in addition to crosswind drift, may cause them to deviate slightly to the right or the left of the true vertical plane in which they are fired. This is corrected by the deflection spot knob 407, as will hereafter he explained. The amount of this deflection is de pendent upon the time of flight and the advance position angle g, as well as by the correction set by the deflection spot knob 407. It is further found that this deflection, which is a function oft and g might, be expressed as a function of angle a, so that the deflection setting pointer 368 would represent a function of t and g, plus deflection spot, or angle (a) plus deflection spot. Formula No. 4.

No correction is required for the distance traveled by the projectile during the first few seconds of its flight, regardless of the direction in which the projectile is fired, but a correction is required for that period of time after the first few seconds because it is known that its velocity varies depending upon whether it is fired horizontally, vertically, or in an intermediate direction. Therefore, certain parts are moved in accordance with a function of time instead of the value 2, as will be hereinafter ex plained.

It is impracticable to give an exact equation for Formula No. 4, for the formula would be variable accord ing to different caliber guns and the information on which any equation would be formulated would be derived from a study of various graphs which would be derived from ballistic data, which ballistic data would vary with different caliber guns. However, the parts shown in the draw ing in this case are drawn substantially to scale to reprc sent one particular caliber.

The sight angle, (a) plus (b) may be calculated from FIGURE 16. A perpendicular is drawn from the point C to the line OD extended, meeting the said line at the point M. The angle DMC is, therefore, a right angle, and the angle MDC is equal to the angle g, while the line DC is equal to Vpt. Considering the small triangle DMC, the line MC equals Vpt sing, and the line DM 5 equals Vp! cos g, whilethe line OD equals Vbt.

Vpt sin g Tan b Vbt+Vpt cos 9 However, in the computer, Vpt is represented in knots, while Vbt is represented in feet per second. 1.689 is the conversion factor from knots to feet per second. It will also be noted that t may be eliminated from the equation. The above equation might, therefore, be written:

1.689Vp-sin 9 The super elevation angle a, not shown in FIGURE 16,

is derived fi'om ballistic data and is a function of time e r and the angle g. The sight angle is the sum of the angles (a) plus (b), so that the sight angle equals:

' 1.689Vp sin 9 -1 q T i (Vb-H.689Vp cos 9, However, this conversion from knots to feet per second is performed by properly proportioning the various parts. of the computer and this formula might, therefore, be written in a simplified form as follows:

Sight angle a+ b Elevation Spot V7) sin y Formula No. 5

The powder fuze is sometimes employed. The computer 7 is adapted. for both mechanical fuzes and powder fuzes.

Powder fuzes burn more rapidly at low altitudes than at high altitudes, because there is a greater oxygen content when the air is more dense than when it is more rarefied,

such as in high altitudes. The rate of the burning of a powder fuze is, therefore, dependent upon time t, altirude I: and the angle g. Or it might be expressed as a function of 2, minus a function of h, multiplied by a function of r times a function of g. Formula No. 6. it is impossible to express this as a general mathematical formula for, the same reasons as discussed in connection with Formula No. 4.

Summarizing the above, the advanced position angle balance pointer 138 is balanced in zero, or midposition, when Vbi sin g--h=0. Formula No. l.

The target position angle balance pointer is balanced in its zero, or midposition when,

" cos 5 Formula. Not 3 The slant rang pointer 91 gives a visual indication of the length of the line Rs, which is the slant range and solves the equation:

cos

Formula. No. 2

Vp sin g -t Si ht angle a+tan Vb I VP cos +Elevation Spot Formula No. 5.

The powder fuze pointer 124 is actuated to represent functions of t, h and g. Formula No. 6.

Casing: The computer consists of various parts, such as levers, racks, pinions and wires, all of which are 84 and 90 which are the shafts for the advance position 4 angle balance pointer, the target position angle balance pointer and the slant range pointer, respectively. The advance position angle balance pointer 138 is secured to its shaft 137 and the upper end of this pointer is behind the window 425. A plate 426 is mounted behind the upper ends of the pointers and is provided with slots, through which extend the pointers 85 and 91. The pointer 85 is the target position angle balance pointer secured to the shaft 84, and the pointer 91 is the slant range pointer secured to the shaft 90. This plate 426 has indicia thereon to show what the pointer indicates such as that the pointer 91 denotes the slant range. Each of said shafts is provided with a spring 427 tending to turn the shaft, and its pointer to its zero position. The powder fuze setting pointer 124, the sight pointer 193 and the defiection setting pointer 368 have the same arrangement as just described. Obviously, side plates would be used to complete the casing, as well as a back plate, not shown, so as to exclude dust and to protect the working parts.

The mechanism of the computer: All of the data is entered into the computer by operating the knobs 407 to 416, inclusive. The parts immediately actuated by these knobs are identical, and a general description may be given of one of them which will apply to all. As shown in FIGURES and 6, a knob 43! is secured to a shaft 431, which has a bearing in the plate 423. Secured to the inner endof the shaft 431 is a pinion 432 which meshes with and drives a rack 433, which is held in engagement with the pinion by a guide clip 434. The rack is secured to a plate 435 from which extend one or more wires 436, which extend to various parts of the instrument.

Preparation time knob 410 and barrage time knob 41] The mathematical equations involved" are as follows:

The preparation time needed prior to actual firing on the enemy aircraft is first set in the preparation time knob 410, FIGURE 1. As shown in FIGURE 9, rotation of the preparation time knob 41!) turns pinion 1 which moves rack 2 which carries wire 3. Wire 3 moves level 5 by means of pin 4. Lever 5 is pivoted on movable pin 6. The lever 5 is also actuated by the rotation of the barrage time knob 411. The knob 411 is secured to pinion 92 which actuates rack 93 which moves wire 94 connected to pin 6 of lever 5. The pin 6 may be considered as a fixed pivot for the lever 5 unless the barrage time knob 411 is actuated, and the pin 4 may be considered as a fixed pivot for lever 5 unless the preparation time knob 410 is actuated. The lever 5 may be considered as an addition lever to add the values set by the knob 411 to the values set by the knob 410.

As shown in FIGURE 1, the preparation time knob 410- is rotated twice as far as the barrage time knob 411 to enter a given number of seconds by each knob. Therefore, when the knob 411'is rotated from its zero to its 5 seconds position, its rack 93 will be moved only half as far as the rack 2 would be moved when the knob 410 is rotated from its zero to its 5 seconds position. By making the scales of knobs 410' and 411 to correct scale, the pin 8 is moved a distance corresponding to the value Tb being the barrage time and Tx being the preparation time in seconds.

The pin 8 carried by the midpoint of lever 5 actuates the wire 7 which is connected to lever 9 by means of pin 10. The lever 9 is pivoted on a movable pin 11 which may be raised or lowered by the actuation of the mechanical fuze setting knob 416, as will hereinafter be explained. Unless, however, the knob 416 is actuated, the pin 11 may be considered as a fixed pivot for the lever 9. When, however, the knob 416 is actuated it raises or lowers the pin 11, as will hereinafter be explained, thereby adding the value t (mechanical fuze time) tothe addition so that the pin l3 carried by the lever 9 moves a distance corresponding to The pin 13 actuates the wire 12 connected to the pin 15 carried by the triangular lever 14.

First muitipiying mechanism 50] The triangular lever 14 is mounted on a fixed pivot stud 16 and at its upper end is provided with a pin 18 from which is suspended link 17. Link 17 carries at its lower end pin 21 which passes through the lower end of link 20 and the lefthand end of link 19. The other'end of link 19 is mounted on pin 22 which is movable, as will hereinafter be described, by the actuation of the target speed knob 414, but unless the said knob 414 is actuated the pin 22 may be considered as a fixed pivot for the link 19. Link 20 is connected to hell crank lever 24 by means of pin 23, the lever 24 being mounted on a fixed pivot stud 25. A spring 24' is connected to lever 14 to take up any free play. Lever 24- carries pin 27 which actuates wire 26.

In FIGURE 2 the pin 21 connecting links 17, 19 and 20 is in axial alignment with the fixed stud 16 which forms a pivot for the lever 1.4. The links 17 and 20 are of equal length. Under these conditions movement of the lever 14 will not impart movement to lever 24 for the link 17 will simply turn on the pin 21. If, however, the target speed knob 414 is actuated, as will hereinafter be described, so as to move pin 22 and link 19 to the left or into the position shown in FIGURES 3 and 9, the pin 21 is moved out of alignment with stud 16. If now the lever 14 should be actuated, the link 17 will be raised or lowered, the pin 21 moving on an arc of a circle, having its center at pin 22 and a radius equal to the length of link 19 between the centers of pins 21 and 22. The link 20 will thus be raised or lowered, actuating the lever 24. The links 17, 19 and 20 and the levers 14 and 24, therefore, constitute a multiplying mechanism 501. It multiplies the value Vp introduced by the target speed knob 414 through link 19 by the sum of the values introduced by the preparation time knob 410, the barrage time knob 411, and the mechanical fuze setting knob 416, so that this product will be In like manner, when the racks 93 and 2 are in the elevated positions as shown in FIGURE 2, corresponding to 3 the pins 18 and 23 will be in axial alignment with each other. If now the pin 22 'and link 19 were moved to the right or left by the actuation of the target speed knob 413 to set in the value Vp the lever 24 would not be rotated, for

and VpXzero=0. However, if the racks 93 and 2 are lowered as shown in FIGURE 9 by the rotation to a value of the preparation time knob 410 and the barrage time knob 411 and/or if the mechanical fuze setting knob 416 is set to represent a value, the lever 14 is rocked anticlockwise or into the position shown in FIGURE 9.

When the racks 2 and 93and the pin 11 are in theirlowermost positions with the lever 14 in its adjusted position with the pins 18 and 23 out of alignment and with the lever 14 stationary, if the pin 22 will move to the right or left by the actuation of the target speed knob 414, as will hereinafter be described, the lever 24 will be rotated on its pivot stud 25 and the amount of the rotation de-= pends upon the distance apart of the pins 18 and 23 multiplied by the movement of the pin 21. The distance apart of the pins 18 and 23 is controlled by the position of the addition lever 9 to add thevalue of the barrage time set by knob 411 to the value of the preparation time set by the knob 410 plus the value introduced by the pin -11 con-= trolled by the mechanical fuze setting knob 41 6. The movement of the pin 27 of the lever 24 is, therefore,

which is the same value as described heretofore.

Wire 26 actuates an arm 28 by means of pin 29 carried by the projection or extension 28' on the arm 28, with arm 28 pivoted on a fixed pivot 30. The wire 26 when in its zero position forms a right angle with the line from the center of pin 29 to the center of pivot 30.

Second multiplying mechanism 502 Arm 28 moves link 31 by means of pin 32. Link 31 carries pin 35 which passes through the lower ends of links 33 and 34. Link 33 is suspended from pin 36 secured by bell crank lever 257, FIGURES 2, 3,8 and 13, which is controlled by the advance position angle knob 409 and the target position angle knob 408, as will hereinafter be described. Link 34 carries a pin 38 at its upper end which pin passes through bell crank lever 37, having a fixed pivot on stud 39. Lever 37 actu-ates wire 40 being connected thereto by pin 41.

As will hereinafter be explained, when the advance po= sition angle knob 409 which enters the value of the angle (g) and the target position angle knob 408 which enters the value of the target position angle (e) are rotated so as to show their maximum possible settings, the lever 257 is rotated so as to bring pin 36 into substantial axial alignment with pin 38. Under such a condition the bell crank lever 37 would not be actuated regardless of how much the lever 28 should be moved. The reason for this is apparent for as the value of the angle g+e approaches 90 so that approaches or equals zero, we would be multiplying Vp( Tz-lt) raised or lowered actuating lever 37, pin 41, and wire 40. The movement apart of pins 36 and 33 enters the value It will also be noted, as shown in the value of i.e., when the barrage time knob which enters the value the preparation time knob which. enters the value Tx,

and the mechanical fuze setting knob which enters the value t are in their zero positions, the pin 35 which conmeets the links 33 and 34 to the link 31 isin alignment withv the pivot stud 259 of the bell crank lever 257. As men tioned above, rotation of the target position angle knob 408 and the advance position angle knob 409 rotates the lever 257 on its pivot stud 259. When the lever 257 is so rotated and if pin 35 is in alignmentwith pivot 259, no movement is imparted to lever 37, but when the pin 35 is out of alignment with the stud 257, as shown in FIGURE 9; i.e., when represents a value greater than zero, the above described.

multiplication results when the lever 257 is actuated.

Third multiplying mechanism 503 This multiplying mechanism is in fact adivision mecha nism. Wire 40 actuates bell crank lever 42 by means of pin 43, bell crank lever 42 being mounted on a fixed pivot I stud 44.- Lever 42 carries a pin 46 on which is mounted. link 45. Link 45 carries at its lower end a pin 49 passing through links 47 and 48, with link 48 being pivoted on pin. 50. A spring 50" is connected to pin 50 so-as to urge the pin 50 to the right to take up any free play. Link 47 carries at its upper end a pin 51 which is also carried by the bell crank lever 231, which enters the value ge cos 2 as will hereinafter be explained in connection with the target position angle knob 408 and the advance position angle knob 400 which knobs serve as a means to rotate the lever 231. Here again we have a multiplying mechanism which may be called the third multiplying mecha nism, and which performs the function of dividing Vp( -l- (Pm-H) cos m cos 5 Since the operation of this third multiplying mechanism is substantially the same as heretofore described, the detailed description is unnecessary.

The pin 50, carried by a link 48, passes, through the upper ends of links 52 and 53, with link 52 being mounted on a fixed pivot stud 55, and the link 53 being mounted on a movable pin 54. The link 53 carries'a pin 57 which actuates the wire 56. As will hereinafter be explained, in connection with the description of the advance position angle knob 409 and the mechanical fuze setting knob 416, the value of the average velocity of the pro- FIGURE 2, that when 

